metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic7⋊C4⋊1C4, C14.62(C4×D4), (C2×C28).49Q8, C14.11(C4×Q8), (C2×C42).5D7, (C2×C28).447D4, (C2×C4).41Dic14, C2.12(C4×Dic14), (C22×C4).396D14, C2.1(C42⋊2D7), C14.54(C22⋊Q8), C14.3(C42.C2), C2.2(C28.6Q8), C14.3(C42⋊2C2), C2.3(C28.48D4), C22.43(C4○D28), C2.14(C42⋊D7), C22.19(C2×Dic14), C23.266(C22×D7), C14.13(C42⋊C2), C14.C42.11C2, (C22×C14).308C23, (C22×C28).473C22, C7⋊5(C23.63C23), C2.1(C23.23D14), C14.55(C22.D4), (C22×Dic7).28C22, (C2×C4×C28).2C2, C2.5(C4×C7⋊D4), (C2×C4).91(C4×D7), (C2×C14).26(C2×Q8), C22.118(C2×C4×D7), (C2×C28).207(C2×C4), (C2×C14).426(C2×D4), C22.41(C2×C7⋊D4), (C2×C14).68(C4○D4), (C2×C4).212(C7⋊D4), (C2×Dic7⋊C4).10C2, (C2×C14).97(C22×C4), (C2×Dic7).26(C2×C4), SmallGroup(448,467)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C42).D7
G = < a,b,c,d,e | a2=b4=c4=d7=1, e2=b2, ebe-1=ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, cd=dc, ece-1=b2c, ede-1=d-1 >
Subgroups: 580 in 154 conjugacy classes, 71 normal (51 characteristic)
C1, C2, C4, C22, C7, C2×C4, C2×C4, C23, C14, C42, C4⋊C4, C22×C4, C22×C4, Dic7, C28, C2×C14, C2.C42, C2×C42, C2×C4⋊C4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, C23.63C23, Dic7⋊C4, Dic7⋊C4, C4×C28, C22×Dic7, C22×C28, C14.C42, C2×Dic7⋊C4, C2×C4×C28, (C2×C42).D7
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C22×C4, C2×D4, C2×Q8, C4○D4, D14, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C22.D4, C42.C2, C42⋊2C2, Dic14, C4×D7, C7⋊D4, C22×D7, C23.63C23, C2×Dic14, C2×C4×D7, C4○D28, C2×C7⋊D4, C4×Dic14, C28.6Q8, C42⋊D7, C42⋊2D7, C28.48D4, C4×C7⋊D4, C23.23D14, (C2×C42).D7
►Regular action on 448 points
Generators in S448
(1 20)(2 21)(3 15)(4 16)(5 17)(6 18)(7 19)(8 22)(9 23)(10 24)(11 25)(12 26)(13 27)(14 28)(29 43)(30 44)(31 45)(32 46)(33 47)(34 48)(35 49)(36 50)(37 51)(38 52)(39 53)(40 54)(41 55)(42 56)(57 71)(58 72)(59 73)(60 74)(61 75)(62 76)(63 77)(64 78)(65 79)(66 80)(67 81)(68 82)(69 83)(70 84)(85 99)(86 100)(87 101)(88 102)(89 103)(90 104)(91 105)(92 106)(93 107)(94 108)(95 109)(96 110)(97 111)(98 112)(113 127)(114 128)(115 129)(116 130)(117 131)(118 132)(119 133)(120 134)(121 135)(122 136)(123 137)(124 138)(125 139)(126 140)(141 155)(142 156)(143 157)(144 158)(145 159)(146 160)(147 161)(148 162)(149 163)(150 164)(151 165)(152 166)(153 167)(154 168)(169 183)(170 184)(171 185)(172 186)(173 187)(174 188)(175 189)(176 190)(177 191)(178 192)(179 193)(180 194)(181 195)(182 196)(197 211)(198 212)(199 213)(200 214)(201 215)(202 216)(203 217)(204 218)(205 219)(206 220)(207 221)(208 222)(209 223)(210 224)(225 239)(226 240)(227 241)(228 242)(229 243)(230 244)(231 245)(232 246)(233 247)(234 248)(235 249)(236 250)(237 251)(238 252)(253 267)(254 268)(255 269)(256 270)(257 271)(258 272)(259 273)(260 274)(261 275)(262 276)(263 277)(264 278)(265 279)(266 280)(281 295)(282 296)(283 297)(284 298)(285 299)(286 300)(287 301)(288 302)(289 303)(290 304)(291 305)(292 306)(293 307)(294 308)(309 323)(310 324)(311 325)(312 326)(313 327)(314 328)(315 329)(316 330)(317 331)(318 332)(319 333)(320 334)(321 335)(322 336)(337 351)(338 352)(339 353)(340 354)(341 355)(342 356)(343 357)(344 358)(345 359)(346 360)(347 361)(348 362)(349 363)(350 364)(365 379)(366 380)(367 381)(368 382)(369 383)(370 384)(371 385)(372 386)(373 387)(374 388)(375 389)(376 390)(377 391)(378 392)(393 407)(394 408)(395 409)(396 410)(397 411)(398 412)(399 413)(400 414)(401 415)(402 416)(403 417)(404 418)(405 419)(406 420)(421 435)(422 436)(423 437)(424 438)(425 439)(426 440)(427 441)(428 442)(429 443)(430 444)(431 445)(432 446)(433 447)(434 448)
(1 125 13 118)(2 126 14 119)(3 120 8 113)(4 121 9 114)(5 122 10 115)(6 123 11 116)(7 124 12 117)(15 134 22 127)(16 135 23 128)(17 136 24 129)(18 137 25 130)(19 138 26 131)(20 139 27 132)(21 140 28 133)(29 148 36 141)(30 149 37 142)(31 150 38 143)(32 151 39 144)(33 152 40 145)(34 153 41 146)(35 154 42 147)(43 162 50 155)(44 163 51 156)(45 164 52 157)(46 165 53 158)(47 166 54 159)(48 167 55 160)(49 168 56 161)(57 176 64 169)(58 177 65 170)(59 178 66 171)(60 179 67 172)(61 180 68 173)(62 181 69 174)(63 182 70 175)(71 190 78 183)(72 191 79 184)(73 192 80 185)(74 193 81 186)(75 194 82 187)(76 195 83 188)(77 196 84 189)(85 204 92 197)(86 205 93 198)(87 206 94 199)(88 207 95 200)(89 208 96 201)(90 209 97 202)(91 210 98 203)(99 218 106 211)(100 219 107 212)(101 220 108 213)(102 221 109 214)(103 222 110 215)(104 223 111 216)(105 224 112 217)(225 358 232 351)(226 359 233 352)(227 360 234 353)(228 361 235 354)(229 362 236 355)(230 363 237 356)(231 364 238 357)(239 344 246 337)(240 345 247 338)(241 346 248 339)(242 347 249 340)(243 348 250 341)(244 349 251 342)(245 350 252 343)(253 386 260 379)(254 387 261 380)(255 388 262 381)(256 389 263 382)(257 390 264 383)(258 391 265 384)(259 392 266 385)(267 372 274 365)(268 373 275 366)(269 374 276 367)(270 375 277 368)(271 376 278 369)(272 377 279 370)(273 378 280 371)(281 414 288 407)(282 415 289 408)(283 416 290 409)(284 417 291 410)(285 418 292 411)(286 419 293 412)(287 420 294 413)(295 400 302 393)(296 401 303 394)(297 402 304 395)(298 403 305 396)(299 404 306 397)(300 405 307 398)(301 406 308 399)(309 442 316 435)(310 443 317 436)(311 444 318 437)(312 445 319 438)(313 446 320 439)(314 447 321 440)(315 448 322 441)(323 428 330 421)(324 429 331 422)(325 430 332 423)(326 431 333 424)(327 432 334 425)(328 433 335 426)(329 434 336 427)
(1 90 34 62)(2 91 35 63)(3 85 29 57)(4 86 30 58)(5 87 31 59)(6 88 32 60)(7 89 33 61)(8 92 36 64)(9 93 37 65)(10 94 38 66)(11 95 39 67)(12 96 40 68)(13 97 41 69)(14 98 42 70)(15 99 43 71)(16 100 44 72)(17 101 45 73)(18 102 46 74)(19 103 47 75)(20 104 48 76)(21 105 49 77)(22 106 50 78)(23 107 51 79)(24 108 52 80)(25 109 53 81)(26 110 54 82)(27 111 55 83)(28 112 56 84)(113 197 141 169)(114 198 142 170)(115 199 143 171)(116 200 144 172)(117 201 145 173)(118 202 146 174)(119 203 147 175)(120 204 148 176)(121 205 149 177)(122 206 150 178)(123 207 151 179)(124 208 152 180)(125 209 153 181)(126 210 154 182)(127 211 155 183)(128 212 156 184)(129 213 157 185)(130 214 158 186)(131 215 159 187)(132 216 160 188)(133 217 161 189)(134 218 162 190)(135 219 163 191)(136 220 164 192)(137 221 165 193)(138 222 166 194)(139 223 167 195)(140 224 168 196)(225 316 253 288)(226 317 254 289)(227 318 255 290)(228 319 256 291)(229 320 257 292)(230 321 258 293)(231 322 259 294)(232 309 260 281)(233 310 261 282)(234 311 262 283)(235 312 263 284)(236 313 264 285)(237 314 265 286)(238 315 266 287)(239 330 267 302)(240 331 268 303)(241 332 269 304)(242 333 270 305)(243 334 271 306)(244 335 272 307)(245 336 273 308)(246 323 274 295)(247 324 275 296)(248 325 276 297)(249 326 277 298)(250 327 278 299)(251 328 279 300)(252 329 280 301)(337 428 365 400)(338 429 366 401)(339 430 367 402)(340 431 368 403)(341 432 369 404)(342 433 370 405)(343 434 371 406)(344 421 372 393)(345 422 373 394)(346 423 374 395)(347 424 375 396)(348 425 376 397)(349 426 377 398)(350 427 378 399)(351 442 379 414)(352 443 380 415)(353 444 381 416)(354 445 382 417)(355 446 383 418)(356 447 384 419)(357 448 385 420)(358 435 386 407)(359 436 387 408)(360 437 388 409)(361 438 389 410)(362 439 390 411)(363 440 391 412)(364 441 392 413)
(1 2 3 4 5 6 7)(8 9 10 11 12 13 14)(15 16 17 18 19 20 21)(22 23 24 25 26 27 28)(29 30 31 32 33 34 35)(36 37 38 39 40 41 42)(43 44 45 46 47 48 49)(50 51 52 53 54 55 56)(57 58 59 60 61 62 63)(64 65 66 67 68 69 70)(71 72 73 74 75 76 77)(78 79 80 81 82 83 84)(85 86 87 88 89 90 91)(92 93 94 95 96 97 98)(99 100 101 102 103 104 105)(106 107 108 109 110 111 112)(113 114 115 116 117 118 119)(120 121 122 123 124 125 126)(127 128 129 130 131 132 133)(134 135 136 137 138 139 140)(141 142 143 144 145 146 147)(148 149 150 151 152 153 154)(155 156 157 158 159 160 161)(162 163 164 165 166 167 168)(169 170 171 172 173 174 175)(176 177 178 179 180 181 182)(183 184 185 186 187 188 189)(190 191 192 193 194 195 196)(197 198 199 200 201 202 203)(204 205 206 207 208 209 210)(211 212 213 214 215 216 217)(218 219 220 221 222 223 224)(225 226 227 228 229 230 231)(232 233 234 235 236 237 238)(239 240 241 242 243 244 245)(246 247 248 249 250 251 252)(253 254 255 256 257 258 259)(260 261 262 263 264 265 266)(267 268 269 270 271 272 273)(274 275 276 277 278 279 280)(281 282 283 284 285 286 287)(288 289 290 291 292 293 294)(295 296 297 298 299 300 301)(302 303 304 305 306 307 308)(309 310 311 312 313 314 315)(316 317 318 319 320 321 322)(323 324 325 326 327 328 329)(330 331 332 333 334 335 336)(337 338 339 340 341 342 343)(344 345 346 347 348 349 350)(351 352 353 354 355 356 357)(358 359 360 361 362 363 364)(365 366 367 368 369 370 371)(372 373 374 375 376 377 378)(379 380 381 382 383 384 385)(386 387 388 389 390 391 392)(393 394 395 396 397 398 399)(400 401 402 403 404 405 406)(407 408 409 410 411 412 413)(414 415 416 417 418 419 420)(421 422 423 424 425 426 427)(428 429 430 431 432 433 434)(435 436 437 438 439 440 441)(442 443 444 445 446 447 448)
(1 238 13 231)(2 237 14 230)(3 236 8 229)(4 235 9 228)(5 234 10 227)(6 233 11 226)(7 232 12 225)(15 250 22 243)(16 249 23 242)(17 248 24 241)(18 247 25 240)(19 246 26 239)(20 252 27 245)(21 251 28 244)(29 264 36 257)(30 263 37 256)(31 262 38 255)(32 261 39 254)(33 260 40 253)(34 266 41 259)(35 265 42 258)(43 278 50 271)(44 277 51 270)(45 276 52 269)(46 275 53 268)(47 274 54 267)(48 280 55 273)(49 279 56 272)(57 292 64 285)(58 291 65 284)(59 290 66 283)(60 289 67 282)(61 288 68 281)(62 294 69 287)(63 293 70 286)(71 306 78 299)(72 305 79 298)(73 304 80 297)(74 303 81 296)(75 302 82 295)(76 308 83 301)(77 307 84 300)(85 320 92 313)(86 319 93 312)(87 318 94 311)(88 317 95 310)(89 316 96 309)(90 322 97 315)(91 321 98 314)(99 334 106 327)(100 333 107 326)(101 332 108 325)(102 331 109 324)(103 330 110 323)(104 336 111 329)(105 335 112 328)(113 348 120 341)(114 347 121 340)(115 346 122 339)(116 345 123 338)(117 344 124 337)(118 350 125 343)(119 349 126 342)(127 362 134 355)(128 361 135 354)(129 360 136 353)(130 359 137 352)(131 358 138 351)(132 364 139 357)(133 363 140 356)(141 376 148 369)(142 375 149 368)(143 374 150 367)(144 373 151 366)(145 372 152 365)(146 378 153 371)(147 377 154 370)(155 390 162 383)(156 389 163 382)(157 388 164 381)(158 387 165 380)(159 386 166 379)(160 392 167 385)(161 391 168 384)(169 404 176 397)(170 403 177 396)(171 402 178 395)(172 401 179 394)(173 400 180 393)(174 406 181 399)(175 405 182 398)(183 418 190 411)(184 417 191 410)(185 416 192 409)(186 415 193 408)(187 414 194 407)(188 420 195 413)(189 419 196 412)(197 432 204 425)(198 431 205 424)(199 430 206 423)(200 429 207 422)(201 428 208 421)(202 434 209 427)(203 433 210 426)(211 446 218 439)(212 445 219 438)(213 444 220 437)(214 443 221 436)(215 442 222 435)(216 448 223 441)(217 447 224 440)
G:=sub<Sym(448)| (1,20)(2,21)(3,15)(4,16)(5,17)(6,18)(7,19)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(113,127)(114,128)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224)(225,239)(226,240)(227,241)(228,242)(229,243)(230,244)(231,245)(232,246)(233,247)(234,248)(235,249)(236,250)(237,251)(238,252)(253,267)(254,268)(255,269)(256,270)(257,271)(258,272)(259,273)(260,274)(261,275)(262,276)(263,277)(264,278)(265,279)(266,280)(281,295)(282,296)(283,297)(284,298)(285,299)(286,300)(287,301)(288,302)(289,303)(290,304)(291,305)(292,306)(293,307)(294,308)(309,323)(310,324)(311,325)(312,326)(313,327)(314,328)(315,329)(316,330)(317,331)(318,332)(319,333)(320,334)(321,335)(322,336)(337,351)(338,352)(339,353)(340,354)(341,355)(342,356)(343,357)(344,358)(345,359)(346,360)(347,361)(348,362)(349,363)(350,364)(365,379)(366,380)(367,381)(368,382)(369,383)(370,384)(371,385)(372,386)(373,387)(374,388)(375,389)(376,390)(377,391)(378,392)(393,407)(394,408)(395,409)(396,410)(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)(405,419)(406,420)(421,435)(422,436)(423,437)(424,438)(425,439)(426,440)(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448), (1,125,13,118)(2,126,14,119)(3,120,8,113)(4,121,9,114)(5,122,10,115)(6,123,11,116)(7,124,12,117)(15,134,22,127)(16,135,23,128)(17,136,24,129)(18,137,25,130)(19,138,26,131)(20,139,27,132)(21,140,28,133)(29,148,36,141)(30,149,37,142)(31,150,38,143)(32,151,39,144)(33,152,40,145)(34,153,41,146)(35,154,42,147)(43,162,50,155)(44,163,51,156)(45,164,52,157)(46,165,53,158)(47,166,54,159)(48,167,55,160)(49,168,56,161)(57,176,64,169)(58,177,65,170)(59,178,66,171)(60,179,67,172)(61,180,68,173)(62,181,69,174)(63,182,70,175)(71,190,78,183)(72,191,79,184)(73,192,80,185)(74,193,81,186)(75,194,82,187)(76,195,83,188)(77,196,84,189)(85,204,92,197)(86,205,93,198)(87,206,94,199)(88,207,95,200)(89,208,96,201)(90,209,97,202)(91,210,98,203)(99,218,106,211)(100,219,107,212)(101,220,108,213)(102,221,109,214)(103,222,110,215)(104,223,111,216)(105,224,112,217)(225,358,232,351)(226,359,233,352)(227,360,234,353)(228,361,235,354)(229,362,236,355)(230,363,237,356)(231,364,238,357)(239,344,246,337)(240,345,247,338)(241,346,248,339)(242,347,249,340)(243,348,250,341)(244,349,251,342)(245,350,252,343)(253,386,260,379)(254,387,261,380)(255,388,262,381)(256,389,263,382)(257,390,264,383)(258,391,265,384)(259,392,266,385)(267,372,274,365)(268,373,275,366)(269,374,276,367)(270,375,277,368)(271,376,278,369)(272,377,279,370)(273,378,280,371)(281,414,288,407)(282,415,289,408)(283,416,290,409)(284,417,291,410)(285,418,292,411)(286,419,293,412)(287,420,294,413)(295,400,302,393)(296,401,303,394)(297,402,304,395)(298,403,305,396)(299,404,306,397)(300,405,307,398)(301,406,308,399)(309,442,316,435)(310,443,317,436)(311,444,318,437)(312,445,319,438)(313,446,320,439)(314,447,321,440)(315,448,322,441)(323,428,330,421)(324,429,331,422)(325,430,332,423)(326,431,333,424)(327,432,334,425)(328,433,335,426)(329,434,336,427), (1,90,34,62)(2,91,35,63)(3,85,29,57)(4,86,30,58)(5,87,31,59)(6,88,32,60)(7,89,33,61)(8,92,36,64)(9,93,37,65)(10,94,38,66)(11,95,39,67)(12,96,40,68)(13,97,41,69)(14,98,42,70)(15,99,43,71)(16,100,44,72)(17,101,45,73)(18,102,46,74)(19,103,47,75)(20,104,48,76)(21,105,49,77)(22,106,50,78)(23,107,51,79)(24,108,52,80)(25,109,53,81)(26,110,54,82)(27,111,55,83)(28,112,56,84)(113,197,141,169)(114,198,142,170)(115,199,143,171)(116,200,144,172)(117,201,145,173)(118,202,146,174)(119,203,147,175)(120,204,148,176)(121,205,149,177)(122,206,150,178)(123,207,151,179)(124,208,152,180)(125,209,153,181)(126,210,154,182)(127,211,155,183)(128,212,156,184)(129,213,157,185)(130,214,158,186)(131,215,159,187)(132,216,160,188)(133,217,161,189)(134,218,162,190)(135,219,163,191)(136,220,164,192)(137,221,165,193)(138,222,166,194)(139,223,167,195)(140,224,168,196)(225,316,253,288)(226,317,254,289)(227,318,255,290)(228,319,256,291)(229,320,257,292)(230,321,258,293)(231,322,259,294)(232,309,260,281)(233,310,261,282)(234,311,262,283)(235,312,263,284)(236,313,264,285)(237,314,265,286)(238,315,266,287)(239,330,267,302)(240,331,268,303)(241,332,269,304)(242,333,270,305)(243,334,271,306)(244,335,272,307)(245,336,273,308)(246,323,274,295)(247,324,275,296)(248,325,276,297)(249,326,277,298)(250,327,278,299)(251,328,279,300)(252,329,280,301)(337,428,365,400)(338,429,366,401)(339,430,367,402)(340,431,368,403)(341,432,369,404)(342,433,370,405)(343,434,371,406)(344,421,372,393)(345,422,373,394)(346,423,374,395)(347,424,375,396)(348,425,376,397)(349,426,377,398)(350,427,378,399)(351,442,379,414)(352,443,380,415)(353,444,381,416)(354,445,382,417)(355,446,383,418)(356,447,384,419)(357,448,385,420)(358,435,386,407)(359,436,387,408)(360,437,388,409)(361,438,389,410)(362,439,390,411)(363,440,391,412)(364,441,392,413), (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21)(22,23,24,25,26,27,28)(29,30,31,32,33,34,35)(36,37,38,39,40,41,42)(43,44,45,46,47,48,49)(50,51,52,53,54,55,56)(57,58,59,60,61,62,63)(64,65,66,67,68,69,70)(71,72,73,74,75,76,77)(78,79,80,81,82,83,84)(85,86,87,88,89,90,91)(92,93,94,95,96,97,98)(99,100,101,102,103,104,105)(106,107,108,109,110,111,112)(113,114,115,116,117,118,119)(120,121,122,123,124,125,126)(127,128,129,130,131,132,133)(134,135,136,137,138,139,140)(141,142,143,144,145,146,147)(148,149,150,151,152,153,154)(155,156,157,158,159,160,161)(162,163,164,165,166,167,168)(169,170,171,172,173,174,175)(176,177,178,179,180,181,182)(183,184,185,186,187,188,189)(190,191,192,193,194,195,196)(197,198,199,200,201,202,203)(204,205,206,207,208,209,210)(211,212,213,214,215,216,217)(218,219,220,221,222,223,224)(225,226,227,228,229,230,231)(232,233,234,235,236,237,238)(239,240,241,242,243,244,245)(246,247,248,249,250,251,252)(253,254,255,256,257,258,259)(260,261,262,263,264,265,266)(267,268,269,270,271,272,273)(274,275,276,277,278,279,280)(281,282,283,284,285,286,287)(288,289,290,291,292,293,294)(295,296,297,298,299,300,301)(302,303,304,305,306,307,308)(309,310,311,312,313,314,315)(316,317,318,319,320,321,322)(323,324,325,326,327,328,329)(330,331,332,333,334,335,336)(337,338,339,340,341,342,343)(344,345,346,347,348,349,350)(351,352,353,354,355,356,357)(358,359,360,361,362,363,364)(365,366,367,368,369,370,371)(372,373,374,375,376,377,378)(379,380,381,382,383,384,385)(386,387,388,389,390,391,392)(393,394,395,396,397,398,399)(400,401,402,403,404,405,406)(407,408,409,410,411,412,413)(414,415,416,417,418,419,420)(421,422,423,424,425,426,427)(428,429,430,431,432,433,434)(435,436,437,438,439,440,441)(442,443,444,445,446,447,448), (1,238,13,231)(2,237,14,230)(3,236,8,229)(4,235,9,228)(5,234,10,227)(6,233,11,226)(7,232,12,225)(15,250,22,243)(16,249,23,242)(17,248,24,241)(18,247,25,240)(19,246,26,239)(20,252,27,245)(21,251,28,244)(29,264,36,257)(30,263,37,256)(31,262,38,255)(32,261,39,254)(33,260,40,253)(34,266,41,259)(35,265,42,258)(43,278,50,271)(44,277,51,270)(45,276,52,269)(46,275,53,268)(47,274,54,267)(48,280,55,273)(49,279,56,272)(57,292,64,285)(58,291,65,284)(59,290,66,283)(60,289,67,282)(61,288,68,281)(62,294,69,287)(63,293,70,286)(71,306,78,299)(72,305,79,298)(73,304,80,297)(74,303,81,296)(75,302,82,295)(76,308,83,301)(77,307,84,300)(85,320,92,313)(86,319,93,312)(87,318,94,311)(88,317,95,310)(89,316,96,309)(90,322,97,315)(91,321,98,314)(99,334,106,327)(100,333,107,326)(101,332,108,325)(102,331,109,324)(103,330,110,323)(104,336,111,329)(105,335,112,328)(113,348,120,341)(114,347,121,340)(115,346,122,339)(116,345,123,338)(117,344,124,337)(118,350,125,343)(119,349,126,342)(127,362,134,355)(128,361,135,354)(129,360,136,353)(130,359,137,352)(131,358,138,351)(132,364,139,357)(133,363,140,356)(141,376,148,369)(142,375,149,368)(143,374,150,367)(144,373,151,366)(145,372,152,365)(146,378,153,371)(147,377,154,370)(155,390,162,383)(156,389,163,382)(157,388,164,381)(158,387,165,380)(159,386,166,379)(160,392,167,385)(161,391,168,384)(169,404,176,397)(170,403,177,396)(171,402,178,395)(172,401,179,394)(173,400,180,393)(174,406,181,399)(175,405,182,398)(183,418,190,411)(184,417,191,410)(185,416,192,409)(186,415,193,408)(187,414,194,407)(188,420,195,413)(189,419,196,412)(197,432,204,425)(198,431,205,424)(199,430,206,423)(200,429,207,422)(201,428,208,421)(202,434,209,427)(203,433,210,426)(211,446,218,439)(212,445,219,438)(213,444,220,437)(214,443,221,436)(215,442,222,435)(216,448,223,441)(217,447,224,440)>;
G:=Group( (1,20)(2,21)(3,15)(4,16)(5,17)(6,18)(7,19)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112)(113,127)(114,128)(115,129)(116,130)(117,131)(118,132)(119,133)(120,134)(121,135)(122,136)(123,137)(124,138)(125,139)(126,140)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224)(225,239)(226,240)(227,241)(228,242)(229,243)(230,244)(231,245)(232,246)(233,247)(234,248)(235,249)(236,250)(237,251)(238,252)(253,267)(254,268)(255,269)(256,270)(257,271)(258,272)(259,273)(260,274)(261,275)(262,276)(263,277)(264,278)(265,279)(266,280)(281,295)(282,296)(283,297)(284,298)(285,299)(286,300)(287,301)(288,302)(289,303)(290,304)(291,305)(292,306)(293,307)(294,308)(309,323)(310,324)(311,325)(312,326)(313,327)(314,328)(315,329)(316,330)(317,331)(318,332)(319,333)(320,334)(321,335)(322,336)(337,351)(338,352)(339,353)(340,354)(341,355)(342,356)(343,357)(344,358)(345,359)(346,360)(347,361)(348,362)(349,363)(350,364)(365,379)(366,380)(367,381)(368,382)(369,383)(370,384)(371,385)(372,386)(373,387)(374,388)(375,389)(376,390)(377,391)(378,392)(393,407)(394,408)(395,409)(396,410)(397,411)(398,412)(399,413)(400,414)(401,415)(402,416)(403,417)(404,418)(405,419)(406,420)(421,435)(422,436)(423,437)(424,438)(425,439)(426,440)(427,441)(428,442)(429,443)(430,444)(431,445)(432,446)(433,447)(434,448), (1,125,13,118)(2,126,14,119)(3,120,8,113)(4,121,9,114)(5,122,10,115)(6,123,11,116)(7,124,12,117)(15,134,22,127)(16,135,23,128)(17,136,24,129)(18,137,25,130)(19,138,26,131)(20,139,27,132)(21,140,28,133)(29,148,36,141)(30,149,37,142)(31,150,38,143)(32,151,39,144)(33,152,40,145)(34,153,41,146)(35,154,42,147)(43,162,50,155)(44,163,51,156)(45,164,52,157)(46,165,53,158)(47,166,54,159)(48,167,55,160)(49,168,56,161)(57,176,64,169)(58,177,65,170)(59,178,66,171)(60,179,67,172)(61,180,68,173)(62,181,69,174)(63,182,70,175)(71,190,78,183)(72,191,79,184)(73,192,80,185)(74,193,81,186)(75,194,82,187)(76,195,83,188)(77,196,84,189)(85,204,92,197)(86,205,93,198)(87,206,94,199)(88,207,95,200)(89,208,96,201)(90,209,97,202)(91,210,98,203)(99,218,106,211)(100,219,107,212)(101,220,108,213)(102,221,109,214)(103,222,110,215)(104,223,111,216)(105,224,112,217)(225,358,232,351)(226,359,233,352)(227,360,234,353)(228,361,235,354)(229,362,236,355)(230,363,237,356)(231,364,238,357)(239,344,246,337)(240,345,247,338)(241,346,248,339)(242,347,249,340)(243,348,250,341)(244,349,251,342)(245,350,252,343)(253,386,260,379)(254,387,261,380)(255,388,262,381)(256,389,263,382)(257,390,264,383)(258,391,265,384)(259,392,266,385)(267,372,274,365)(268,373,275,366)(269,374,276,367)(270,375,277,368)(271,376,278,369)(272,377,279,370)(273,378,280,371)(281,414,288,407)(282,415,289,408)(283,416,290,409)(284,417,291,410)(285,418,292,411)(286,419,293,412)(287,420,294,413)(295,400,302,393)(296,401,303,394)(297,402,304,395)(298,403,305,396)(299,404,306,397)(300,405,307,398)(301,406,308,399)(309,442,316,435)(310,443,317,436)(311,444,318,437)(312,445,319,438)(313,446,320,439)(314,447,321,440)(315,448,322,441)(323,428,330,421)(324,429,331,422)(325,430,332,423)(326,431,333,424)(327,432,334,425)(328,433,335,426)(329,434,336,427), (1,90,34,62)(2,91,35,63)(3,85,29,57)(4,86,30,58)(5,87,31,59)(6,88,32,60)(7,89,33,61)(8,92,36,64)(9,93,37,65)(10,94,38,66)(11,95,39,67)(12,96,40,68)(13,97,41,69)(14,98,42,70)(15,99,43,71)(16,100,44,72)(17,101,45,73)(18,102,46,74)(19,103,47,75)(20,104,48,76)(21,105,49,77)(22,106,50,78)(23,107,51,79)(24,108,52,80)(25,109,53,81)(26,110,54,82)(27,111,55,83)(28,112,56,84)(113,197,141,169)(114,198,142,170)(115,199,143,171)(116,200,144,172)(117,201,145,173)(118,202,146,174)(119,203,147,175)(120,204,148,176)(121,205,149,177)(122,206,150,178)(123,207,151,179)(124,208,152,180)(125,209,153,181)(126,210,154,182)(127,211,155,183)(128,212,156,184)(129,213,157,185)(130,214,158,186)(131,215,159,187)(132,216,160,188)(133,217,161,189)(134,218,162,190)(135,219,163,191)(136,220,164,192)(137,221,165,193)(138,222,166,194)(139,223,167,195)(140,224,168,196)(225,316,253,288)(226,317,254,289)(227,318,255,290)(228,319,256,291)(229,320,257,292)(230,321,258,293)(231,322,259,294)(232,309,260,281)(233,310,261,282)(234,311,262,283)(235,312,263,284)(236,313,264,285)(237,314,265,286)(238,315,266,287)(239,330,267,302)(240,331,268,303)(241,332,269,304)(242,333,270,305)(243,334,271,306)(244,335,272,307)(245,336,273,308)(246,323,274,295)(247,324,275,296)(248,325,276,297)(249,326,277,298)(250,327,278,299)(251,328,279,300)(252,329,280,301)(337,428,365,400)(338,429,366,401)(339,430,367,402)(340,431,368,403)(341,432,369,404)(342,433,370,405)(343,434,371,406)(344,421,372,393)(345,422,373,394)(346,423,374,395)(347,424,375,396)(348,425,376,397)(349,426,377,398)(350,427,378,399)(351,442,379,414)(352,443,380,415)(353,444,381,416)(354,445,382,417)(355,446,383,418)(356,447,384,419)(357,448,385,420)(358,435,386,407)(359,436,387,408)(360,437,388,409)(361,438,389,410)(362,439,390,411)(363,440,391,412)(364,441,392,413), (1,2,3,4,5,6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21)(22,23,24,25,26,27,28)(29,30,31,32,33,34,35)(36,37,38,39,40,41,42)(43,44,45,46,47,48,49)(50,51,52,53,54,55,56)(57,58,59,60,61,62,63)(64,65,66,67,68,69,70)(71,72,73,74,75,76,77)(78,79,80,81,82,83,84)(85,86,87,88,89,90,91)(92,93,94,95,96,97,98)(99,100,101,102,103,104,105)(106,107,108,109,110,111,112)(113,114,115,116,117,118,119)(120,121,122,123,124,125,126)(127,128,129,130,131,132,133)(134,135,136,137,138,139,140)(141,142,143,144,145,146,147)(148,149,150,151,152,153,154)(155,156,157,158,159,160,161)(162,163,164,165,166,167,168)(169,170,171,172,173,174,175)(176,177,178,179,180,181,182)(183,184,185,186,187,188,189)(190,191,192,193,194,195,196)(197,198,199,200,201,202,203)(204,205,206,207,208,209,210)(211,212,213,214,215,216,217)(218,219,220,221,222,223,224)(225,226,227,228,229,230,231)(232,233,234,235,236,237,238)(239,240,241,242,243,244,245)(246,247,248,249,250,251,252)(253,254,255,256,257,258,259)(260,261,262,263,264,265,266)(267,268,269,270,271,272,273)(274,275,276,277,278,279,280)(281,282,283,284,285,286,287)(288,289,290,291,292,293,294)(295,296,297,298,299,300,301)(302,303,304,305,306,307,308)(309,310,311,312,313,314,315)(316,317,318,319,320,321,322)(323,324,325,326,327,328,329)(330,331,332,333,334,335,336)(337,338,339,340,341,342,343)(344,345,346,347,348,349,350)(351,352,353,354,355,356,357)(358,359,360,361,362,363,364)(365,366,367,368,369,370,371)(372,373,374,375,376,377,378)(379,380,381,382,383,384,385)(386,387,388,389,390,391,392)(393,394,395,396,397,398,399)(400,401,402,403,404,405,406)(407,408,409,410,411,412,413)(414,415,416,417,418,419,420)(421,422,423,424,425,426,427)(428,429,430,431,432,433,434)(435,436,437,438,439,440,441)(442,443,444,445,446,447,448), (1,238,13,231)(2,237,14,230)(3,236,8,229)(4,235,9,228)(5,234,10,227)(6,233,11,226)(7,232,12,225)(15,250,22,243)(16,249,23,242)(17,248,24,241)(18,247,25,240)(19,246,26,239)(20,252,27,245)(21,251,28,244)(29,264,36,257)(30,263,37,256)(31,262,38,255)(32,261,39,254)(33,260,40,253)(34,266,41,259)(35,265,42,258)(43,278,50,271)(44,277,51,270)(45,276,52,269)(46,275,53,268)(47,274,54,267)(48,280,55,273)(49,279,56,272)(57,292,64,285)(58,291,65,284)(59,290,66,283)(60,289,67,282)(61,288,68,281)(62,294,69,287)(63,293,70,286)(71,306,78,299)(72,305,79,298)(73,304,80,297)(74,303,81,296)(75,302,82,295)(76,308,83,301)(77,307,84,300)(85,320,92,313)(86,319,93,312)(87,318,94,311)(88,317,95,310)(89,316,96,309)(90,322,97,315)(91,321,98,314)(99,334,106,327)(100,333,107,326)(101,332,108,325)(102,331,109,324)(103,330,110,323)(104,336,111,329)(105,335,112,328)(113,348,120,341)(114,347,121,340)(115,346,122,339)(116,345,123,338)(117,344,124,337)(118,350,125,343)(119,349,126,342)(127,362,134,355)(128,361,135,354)(129,360,136,353)(130,359,137,352)(131,358,138,351)(132,364,139,357)(133,363,140,356)(141,376,148,369)(142,375,149,368)(143,374,150,367)(144,373,151,366)(145,372,152,365)(146,378,153,371)(147,377,154,370)(155,390,162,383)(156,389,163,382)(157,388,164,381)(158,387,165,380)(159,386,166,379)(160,392,167,385)(161,391,168,384)(169,404,176,397)(170,403,177,396)(171,402,178,395)(172,401,179,394)(173,400,180,393)(174,406,181,399)(175,405,182,398)(183,418,190,411)(184,417,191,410)(185,416,192,409)(186,415,193,408)(187,414,194,407)(188,420,195,413)(189,419,196,412)(197,432,204,425)(198,431,205,424)(199,430,206,423)(200,429,207,422)(201,428,208,421)(202,434,209,427)(203,433,210,426)(211,446,218,439)(212,445,219,438)(213,444,220,437)(214,443,221,436)(215,442,222,435)(216,448,223,441)(217,447,224,440) );
G=PermutationGroup([[(1,20),(2,21),(3,15),(4,16),(5,17),(6,18),(7,19),(8,22),(9,23),(10,24),(11,25),(12,26),(13,27),(14,28),(29,43),(30,44),(31,45),(32,46),(33,47),(34,48),(35,49),(36,50),(37,51),(38,52),(39,53),(40,54),(41,55),(42,56),(57,71),(58,72),(59,73),(60,74),(61,75),(62,76),(63,77),(64,78),(65,79),(66,80),(67,81),(68,82),(69,83),(70,84),(85,99),(86,100),(87,101),(88,102),(89,103),(90,104),(91,105),(92,106),(93,107),(94,108),(95,109),(96,110),(97,111),(98,112),(113,127),(114,128),(115,129),(116,130),(117,131),(118,132),(119,133),(120,134),(121,135),(122,136),(123,137),(124,138),(125,139),(126,140),(141,155),(142,156),(143,157),(144,158),(145,159),(146,160),(147,161),(148,162),(149,163),(150,164),(151,165),(152,166),(153,167),(154,168),(169,183),(170,184),(171,185),(172,186),(173,187),(174,188),(175,189),(176,190),(177,191),(178,192),(179,193),(180,194),(181,195),(182,196),(197,211),(198,212),(199,213),(200,214),(201,215),(202,216),(203,217),(204,218),(205,219),(206,220),(207,221),(208,222),(209,223),(210,224),(225,239),(226,240),(227,241),(228,242),(229,243),(230,244),(231,245),(232,246),(233,247),(234,248),(235,249),(236,250),(237,251),(238,252),(253,267),(254,268),(255,269),(256,270),(257,271),(258,272),(259,273),(260,274),(261,275),(262,276),(263,277),(264,278),(265,279),(266,280),(281,295),(282,296),(283,297),(284,298),(285,299),(286,300),(287,301),(288,302),(289,303),(290,304),(291,305),(292,306),(293,307),(294,308),(309,323),(310,324),(311,325),(312,326),(313,327),(314,328),(315,329),(316,330),(317,331),(318,332),(319,333),(320,334),(321,335),(322,336),(337,351),(338,352),(339,353),(340,354),(341,355),(342,356),(343,357),(344,358),(345,359),(346,360),(347,361),(348,362),(349,363),(350,364),(365,379),(366,380),(367,381),(368,382),(369,383),(370,384),(371,385),(372,386),(373,387),(374,388),(375,389),(376,390),(377,391),(378,392),(393,407),(394,408),(395,409),(396,410),(397,411),(398,412),(399,413),(400,414),(401,415),(402,416),(403,417),(404,418),(405,419),(406,420),(421,435),(422,436),(423,437),(424,438),(425,439),(426,440),(427,441),(428,442),(429,443),(430,444),(431,445),(432,446),(433,447),(434,448)], [(1,125,13,118),(2,126,14,119),(3,120,8,113),(4,121,9,114),(5,122,10,115),(6,123,11,116),(7,124,12,117),(15,134,22,127),(16,135,23,128),(17,136,24,129),(18,137,25,130),(19,138,26,131),(20,139,27,132),(21,140,28,133),(29,148,36,141),(30,149,37,142),(31,150,38,143),(32,151,39,144),(33,152,40,145),(34,153,41,146),(35,154,42,147),(43,162,50,155),(44,163,51,156),(45,164,52,157),(46,165,53,158),(47,166,54,159),(48,167,55,160),(49,168,56,161),(57,176,64,169),(58,177,65,170),(59,178,66,171),(60,179,67,172),(61,180,68,173),(62,181,69,174),(63,182,70,175),(71,190,78,183),(72,191,79,184),(73,192,80,185),(74,193,81,186),(75,194,82,187),(76,195,83,188),(77,196,84,189),(85,204,92,197),(86,205,93,198),(87,206,94,199),(88,207,95,200),(89,208,96,201),(90,209,97,202),(91,210,98,203),(99,218,106,211),(100,219,107,212),(101,220,108,213),(102,221,109,214),(103,222,110,215),(104,223,111,216),(105,224,112,217),(225,358,232,351),(226,359,233,352),(227,360,234,353),(228,361,235,354),(229,362,236,355),(230,363,237,356),(231,364,238,357),(239,344,246,337),(240,345,247,338),(241,346,248,339),(242,347,249,340),(243,348,250,341),(244,349,251,342),(245,350,252,343),(253,386,260,379),(254,387,261,380),(255,388,262,381),(256,389,263,382),(257,390,264,383),(258,391,265,384),(259,392,266,385),(267,372,274,365),(268,373,275,366),(269,374,276,367),(270,375,277,368),(271,376,278,369),(272,377,279,370),(273,378,280,371),(281,414,288,407),(282,415,289,408),(283,416,290,409),(284,417,291,410),(285,418,292,411),(286,419,293,412),(287,420,294,413),(295,400,302,393),(296,401,303,394),(297,402,304,395),(298,403,305,396),(299,404,306,397),(300,405,307,398),(301,406,308,399),(309,442,316,435),(310,443,317,436),(311,444,318,437),(312,445,319,438),(313,446,320,439),(314,447,321,440),(315,448,322,441),(323,428,330,421),(324,429,331,422),(325,430,332,423),(326,431,333,424),(327,432,334,425),(328,433,335,426),(329,434,336,427)], [(1,90,34,62),(2,91,35,63),(3,85,29,57),(4,86,30,58),(5,87,31,59),(6,88,32,60),(7,89,33,61),(8,92,36,64),(9,93,37,65),(10,94,38,66),(11,95,39,67),(12,96,40,68),(13,97,41,69),(14,98,42,70),(15,99,43,71),(16,100,44,72),(17,101,45,73),(18,102,46,74),(19,103,47,75),(20,104,48,76),(21,105,49,77),(22,106,50,78),(23,107,51,79),(24,108,52,80),(25,109,53,81),(26,110,54,82),(27,111,55,83),(28,112,56,84),(113,197,141,169),(114,198,142,170),(115,199,143,171),(116,200,144,172),(117,201,145,173),(118,202,146,174),(119,203,147,175),(120,204,148,176),(121,205,149,177),(122,206,150,178),(123,207,151,179),(124,208,152,180),(125,209,153,181),(126,210,154,182),(127,211,155,183),(128,212,156,184),(129,213,157,185),(130,214,158,186),(131,215,159,187),(132,216,160,188),(133,217,161,189),(134,218,162,190),(135,219,163,191),(136,220,164,192),(137,221,165,193),(138,222,166,194),(139,223,167,195),(140,224,168,196),(225,316,253,288),(226,317,254,289),(227,318,255,290),(228,319,256,291),(229,320,257,292),(230,321,258,293),(231,322,259,294),(232,309,260,281),(233,310,261,282),(234,311,262,283),(235,312,263,284),(236,313,264,285),(237,314,265,286),(238,315,266,287),(239,330,267,302),(240,331,268,303),(241,332,269,304),(242,333,270,305),(243,334,271,306),(244,335,272,307),(245,336,273,308),(246,323,274,295),(247,324,275,296),(248,325,276,297),(249,326,277,298),(250,327,278,299),(251,328,279,300),(252,329,280,301),(337,428,365,400),(338,429,366,401),(339,430,367,402),(340,431,368,403),(341,432,369,404),(342,433,370,405),(343,434,371,406),(344,421,372,393),(345,422,373,394),(346,423,374,395),(347,424,375,396),(348,425,376,397),(349,426,377,398),(350,427,378,399),(351,442,379,414),(352,443,380,415),(353,444,381,416),(354,445,382,417),(355,446,383,418),(356,447,384,419),(357,448,385,420),(358,435,386,407),(359,436,387,408),(360,437,388,409),(361,438,389,410),(362,439,390,411),(363,440,391,412),(364,441,392,413)], [(1,2,3,4,5,6,7),(8,9,10,11,12,13,14),(15,16,17,18,19,20,21),(22,23,24,25,26,27,28),(29,30,31,32,33,34,35),(36,37,38,39,40,41,42),(43,44,45,46,47,48,49),(50,51,52,53,54,55,56),(57,58,59,60,61,62,63),(64,65,66,67,68,69,70),(71,72,73,74,75,76,77),(78,79,80,81,82,83,84),(85,86,87,88,89,90,91),(92,93,94,95,96,97,98),(99,100,101,102,103,104,105),(106,107,108,109,110,111,112),(113,114,115,116,117,118,119),(120,121,122,123,124,125,126),(127,128,129,130,131,132,133),(134,135,136,137,138,139,140),(141,142,143,144,145,146,147),(148,149,150,151,152,153,154),(155,156,157,158,159,160,161),(162,163,164,165,166,167,168),(169,170,171,172,173,174,175),(176,177,178,179,180,181,182),(183,184,185,186,187,188,189),(190,191,192,193,194,195,196),(197,198,199,200,201,202,203),(204,205,206,207,208,209,210),(211,212,213,214,215,216,217),(218,219,220,221,222,223,224),(225,226,227,228,229,230,231),(232,233,234,235,236,237,238),(239,240,241,242,243,244,245),(246,247,248,249,250,251,252),(253,254,255,256,257,258,259),(260,261,262,263,264,265,266),(267,268,269,270,271,272,273),(274,275,276,277,278,279,280),(281,282,283,284,285,286,287),(288,289,290,291,292,293,294),(295,296,297,298,299,300,301),(302,303,304,305,306,307,308),(309,310,311,312,313,314,315),(316,317,318,319,320,321,322),(323,324,325,326,327,328,329),(330,331,332,333,334,335,336),(337,338,339,340,341,342,343),(344,345,346,347,348,349,350),(351,352,353,354,355,356,357),(358,359,360,361,362,363,364),(365,366,367,368,369,370,371),(372,373,374,375,376,377,378),(379,380,381,382,383,384,385),(386,387,388,389,390,391,392),(393,394,395,396,397,398,399),(400,401,402,403,404,405,406),(407,408,409,410,411,412,413),(414,415,416,417,418,419,420),(421,422,423,424,425,426,427),(428,429,430,431,432,433,434),(435,436,437,438,439,440,441),(442,443,444,445,446,447,448)], [(1,238,13,231),(2,237,14,230),(3,236,8,229),(4,235,9,228),(5,234,10,227),(6,233,11,226),(7,232,12,225),(15,250,22,243),(16,249,23,242),(17,248,24,241),(18,247,25,240),(19,246,26,239),(20,252,27,245),(21,251,28,244),(29,264,36,257),(30,263,37,256),(31,262,38,255),(32,261,39,254),(33,260,40,253),(34,266,41,259),(35,265,42,258),(43,278,50,271),(44,277,51,270),(45,276,52,269),(46,275,53,268),(47,274,54,267),(48,280,55,273),(49,279,56,272),(57,292,64,285),(58,291,65,284),(59,290,66,283),(60,289,67,282),(61,288,68,281),(62,294,69,287),(63,293,70,286),(71,306,78,299),(72,305,79,298),(73,304,80,297),(74,303,81,296),(75,302,82,295),(76,308,83,301),(77,307,84,300),(85,320,92,313),(86,319,93,312),(87,318,94,311),(88,317,95,310),(89,316,96,309),(90,322,97,315),(91,321,98,314),(99,334,106,327),(100,333,107,326),(101,332,108,325),(102,331,109,324),(103,330,110,323),(104,336,111,329),(105,335,112,328),(113,348,120,341),(114,347,121,340),(115,346,122,339),(116,345,123,338),(117,344,124,337),(118,350,125,343),(119,349,126,342),(127,362,134,355),(128,361,135,354),(129,360,136,353),(130,359,137,352),(131,358,138,351),(132,364,139,357),(133,363,140,356),(141,376,148,369),(142,375,149,368),(143,374,150,367),(144,373,151,366),(145,372,152,365),(146,378,153,371),(147,377,154,370),(155,390,162,383),(156,389,163,382),(157,388,164,381),(158,387,165,380),(159,386,166,379),(160,392,167,385),(161,391,168,384),(169,404,176,397),(170,403,177,396),(171,402,178,395),(172,401,179,394),(173,400,180,393),(174,406,181,399),(175,405,182,398),(183,418,190,411),(184,417,191,410),(185,416,192,409),(186,415,193,408),(187,414,194,407),(188,420,195,413),(189,419,196,412),(197,432,204,425),(198,431,205,424),(199,430,206,423),(200,429,207,422),(201,428,208,421),(202,434,209,427),(203,433,210,426),(211,446,218,439),(212,445,219,438),(213,444,220,437),(214,443,221,436),(215,442,222,435),(216,448,223,441),(217,447,224,440)]])
124 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4L | 4M | ··· | 4T | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28BT |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C4 | D4 | Q8 | D7 | C4○D4 | D14 | Dic14 | C4×D7 | C7⋊D4 | C4○D28 |
| kernel | (C2×C42).D7 | C14.C42 | C2×Dic7⋊C4 | C2×C4×C28 | Dic7⋊C4 | C2×C28 | C2×C28 | C2×C42 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C2×C4 | C22 |
| # reps | 1 | 4 | 2 | 1 | 8 | 2 | 2 | 3 | 8 | 9 | 12 | 12 | 12 | 48 |
Matrix representation of (C2×C42).D7 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 13 | 5 | 0 | 0 | 0 | 0 |
| 24 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 16 | 24 | 0 | 0 | 0 | 0 |
| 5 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 11 |
| 0 | 0 | 0 | 0 | 13 | 28 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 28 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 0 | 0 | 0 |
| 0 | 0 | 14 | 20 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 1 |
| 0 | 0 | 0 | 0 | 17 | 8 |
| 22 | 7 | 0 | 0 | 0 | 0 |
| 26 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 5 | 18 | 0 | 0 |
| 0 | 0 | 18 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 22 |
| 0 | 0 | 0 | 0 | 5 | 11 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[13,24,0,0,0,0,5,16,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[16,5,0,0,0,0,24,13,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,1,13,0,0,0,0,11,28],[0,28,0,0,0,0,1,18,0,0,0,0,0,0,16,14,0,0,0,0,0,20,0,0,0,0,0,0,24,17,0,0,0,0,1,8],[22,26,0,0,0,0,7,7,0,0,0,0,0,0,5,18,0,0,0,0,18,24,0,0,0,0,0,0,18,5,0,0,0,0,22,11] >;
(C2×C42).D7 in GAP, Magma, Sage, TeX
(C_2\times C_4^2).D_7
% in TeX
G:=Group("(C2xC4^2).D7"); // GroupNames label
G:=SmallGroup(448,467);
// by ID
G=gap.SmallGroup(448,467);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,253,232,758,58,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=c^4=d^7=1,e^2=b^2,e*b*e^-1=a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,c*d=d*c,e*c*e^-1=b^2*c,e*d*e^-1=d^-1>;
// generators/relations